The intensity ratio in the interference pattern is `1 : 9`. What is the amplitude ratio and the ratio of widths of two slits ?

Answer

`2 : 1 ; 4 : 1`

Explanation

`(I_(min))/(I_(max)) = ((a - b)^(2))/((a + b)^(2)) = (1)/(9)`
`:. (a - b)/(a + b) = (1)/(3) or 3 a - 3 b = a + b`
`2 a = 4b or a = 2 b`
Amplitude ratio : `(a)/(b) = (2)/(1)`
`(w_(1))/(w_(2)) = (I_(1))/(I_(2)) = (a^(2))/(b^(2)) = ((2)/(1))^(2) = 4 : 1`